The flat stable module category of a coherent ring

2014/12/12 by Gillespie, James
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1412.4085

Abstract

Let R by a right coherent ring and R-Mod denote the category of left R-modules. We show that there is an abelian model structure on R-Mod whose cofibrant objects are precisely the Gorenstein flat modules. Employing a new method for constructing model structures, the key step is to show that a module is flat and cotorsion if and only if it is Gorenstein flat and Gorenstein cotorsion.

Related

• Gorenstein flat modules with respect to duality pairs
• Gorenstein flat representations of left rooted quivers
• AC-Gorenstein rings and their stable module categories
• The stable module category of a general ring
• Purity, ascent, and periodicity for Gorenstein flat cotorsion modules